Hello @Neil Singer , the term (Qd Cd)'[x] means d(Qc Cd) /dx. I tried to correct the code, but maybe my syntax is wrong:
DSolve[{Derivative[1][Qd Cd][x] == kd (-Cd[x] + Ci[x]),
Derivative[1][Qd][x] == ko (Cd[x] - Ci[x]),
Qa Derivative[1][Ca][x] == ka Ca[x],
ka Ca[x] == kd (-Cd[x] + Ci[x])}, {Qd[x], Cd[x], Ca[x], Ci[x]}, x]
and with:
DSolve[{D[Qd[x] Cd[x], x] == kd (-Cd[x] + Ci[x]),
Derivative[1][Qd][x] == ko (Cd[x] - Ci[x]),
Qa Derivative[1][Ca][x] == ka Ca[x],
ka Ca[x] == kd (-Cd[x] + Ci[x])}, {Qd[x], Cd[x], Ca[x], Ci[x]}, x]
Thank you so much.